It means "I am called...." Such ways of saying one's name are common in other languages, as well. Take Spanish or French, for example.

As to the '-라고' ending, '라' is a variant of '-다' (from the typical '-다' style of address: -(ㄴ/는)다 (statement), -(으)라 (command), -자 (let's...), -(느)냐 (question)) when used with the copula verb, 이다. The '-고' ending on that in turn indicates that it is quoted speech. So '...(이)라고' followed by any verb indicating speech or reporting something means "says is..." or "is called...."